Question

If sin2AcosBsinC=sinB.sin(A+C) then tanAtanB,tanC are in

Answer 1

Step-by-step explanation:

Given

In ΔABC 

tanA:tanB:tanC=3:4:5 

⟹tanA=3k, tanB=4k, tanC=5k

We know that  

In ΔABC 

∑tanA=ΠtanA

⟹3k+4k+5k=(3k)(4k)(5k)

⟹12k=60k3

⟹5k2=1

⟹k=51 

⟹tanA=53, tanB=54, tanC=55

⟹sinA=5+93, sinB=5+164,sinC=5+25